Brake cooling estimation methods and systems

ABSTRACT

Systems and methods for estimating the cooling time of a brake assembly are disclosed. Systems are provided comprising a processor, a tangible, non-transitory memory configured to communicate with the processor, the tangible, non-transitory memory having instructions stored thereon that, in response to execution by the processor, cause the processor to perform operations comprising receiving, by the processor, a first temperature of a brake assembly at a first time, receiving, by the processor, a second temperature of a brake assembly at a second time, wherein the second time occurs a fixed period after the first time, determining, by the processor, a temperature decay coefficient (“α”) of the brake assembly based on the first temperature and the second temperature and calculating, by the processor, an estimated total time to cool the brake assembly to a predetermined temperature based on the first temperature, the predetermined temperature and α.

FIELD

The present disclosure relates to methods and systems for the estimationof a cooling time for brakes.

BACKGROUND

During brake use, such as during an aircraft landing, brakes convertkinetic energy of a moving vehicle into, among other things, thermalenergy. Brake temperatures thus rise during braking. In aircraft brakes,brakes may reach high temperatures (e.g. well above 1,000° F.). After alanding or other use of aircraft brakes, it is preferable to allow theaircraft brake temperature to cool to a predetermined temperature priorto attempting a take-off.

In that manner, if a take-off is aborted, the aircraft brakes may moresafely accept the heat associated with a “rejected take-off” (“RTO”). AnRTO refers generally to engagement of aircraft brakes during an abortedtake-off. Typically, an RTO includes high braking loads over a shorttime period, which in turn correlates to a rapid increase in braketemperature. If aircraft brakes above the predetermined temperature areused in an RTO, brake malfunction may become more likely. Waiting afixed period of time between landing and take-off tends to lead towasted time, as the brakes may have cooled to the predeterminedtemperature prior to the end of the waiting period.

SUMMARY

Systems are provided comprising a processor, a tangible, non-transitorymemory configured to communicate with the processor, the tangible,non-transitory memory having instructions stored thereon that, inresponse to execution by the processor, cause the processor to performoperations comprising receiving, by the processor, a first temperatureof a brake assembly at a first time, receiving, by the processor, asecond temperature of a brake assembly at a second time, wherein thesecond time occurs a fixed period after the first time, determining, bythe processor, a temperature decay coefficient (“α”) of the brakeassembly using the first temperature and the second temperature andcalculating, by the processor, an estimated total time to cool the brakeassembly to a predetermined temperature based on the first temperature,the predetermined temperature and α.

Methods disclosed include estimating a cooling time of a brake assembly.The method includes a method of estimating a cooling time of a brakeassembly, comprising, receiving, by a brake system control unit (“BSCU”)comprising a processor and a tangible, non-transitory memory, a firsttemperature of the brake assembly at a first time, receiving, by theBSCU, a second temperature of the brake assembly at a second time,determining, by the BSCU, a temperature decay coefficient (“α”) of thebrake assembly using the first temperature and the second temperature,calculating, by the BSCU, an estimated total time to cool the brakeassembly to a predetermined temperature based on a, the firsttemperature and the predetermined temperature.

BRIEF DESCRIPTION OF THE DRAWINGS

The subject matter of the present disclosure is particularly pointed outand distinctly claimed in the concluding portion of the specification. Amore complete understanding of the present disclosure, however, may bestbe obtained by referring to the detailed description and claims whenconsidered in connection with the drawing figures, wherein like numeralsdenote like elements.

FIG. 1 illustrates a brake control unit, in accordance with variousembodiments;

FIG. 2 illustrates a logical flowchart of activation of a system toestimate the time to cool a brake assembly in accordance with variousembodiments; and

FIG. 3 illustrates a logical flow chart for an output of the estimatedtime to cool a brake assembly, in accordance with various embodiments.

DETAILED DESCRIPTION

The detailed description of exemplary embodiments herein makes referenceto the accompanying drawings, which show exemplary embodiments by way ofillustration and their best mode. While these exemplary embodiments aredescribed in sufficient detail to enable those skilled in the art topractice the disclosure, it should be understood that other embodimentsmay be realized and that logical, electrical, and mechanical changes maybe made without departing from the spirit and scope of the disclosure.Thus, the detailed description herein is presented for purposes ofillustration only and not of limitation. For example, the steps recitedin any of the method or process descriptions may be executed in anyorder and are not necessarily limited to the order presented.Furthermore, any reference to singular includes plural embodiments, andany reference to more than one component or step may include a singularembodiment or step. Also, any reference to attached, fixed, connected orthe like may include permanent, removable, temporary, partial, fulland/or any other possible attachment option. Additionally, any referenceto “without contact” (or similar phrases) may also include reducedcontact or minimal contact.

After a landing or other braking event, it is important to determine howmuch time should elapse until the brakes are below a predeterminedtemperature to allow for a safe take-off. Waiting for too long a periodtends to waste time, which is not acceptable in the time-sensitiveaviation industry. Waiting for too short a period may compromiseaviation safety.

The thermodynamics of a brake assembly (i.e., brake heat sink, pressureplate, and/or other components) are complex systems to model.Sophisticated models that incorporate many environmental variables andother data may be used with a high level of accuracy. However, suchsophisticated models are associated with systems that are capable ofproviding a wide number of environmental variables and utilizesignificant processor and memory overhead. Such systems also tend torely on a constant power supply during operation. Thus, powerinterruption may impair the ability of such a system to function. Asdisclosed in various embodiments, various systems and methods may beused to estimate a time for a brake to cool without using, for example,the ambient temperature. In this manner, various embodiments use lowsystem overhead (e.g., small amounts of memory and/or processor time)and are robust enough to withstand intermittent power interruptions.

After a brake assembly has reached a peak temperature, calculating anestimated total time to cool may be simplified with the assumption thatthe cooling profile of the brake assembly mainly follows a convectiveprocess. Moreover, ambient air temperature may be excluded fromcalculations in various embodiments without (or with minimal)sacrificing accuracy. By excluding ambient air temperature, one need nothave access to a sensor that provides ambient air temperature, nor theassociated processor overhead for receiving ambient air temperature andprocessing the same. Instead, tuning parameters may be used to tune thetime to cool estimation.

Temperature measurements of a brake assembly may be taken periodically.For example, time t_(n) may be found using the number of measurementstaken multiplied by the time of the period. Stated another way,t_(n)=nT_(period) where n is the number of measurements (i.e., samples)taken and T_(period) is the length of the period between eachmeasurement (i.e., a length of a sampling period). For example, where 5measurements have been taken (n=5) at one minute intervals (T_(period)=1minute), time t_(n) is 5 minutes. The sampling period is notparticularly limited and, in various embodiments, may include periods of5 minutes, 2 minutes, 1 minute, 45 seconds, 30 seconds, and 15 seconds.

In various embodiments, by using the ratio of the temperature of thebrake assembly for two samples, α, a temperature decay coefficientgreater than zero, may be determined and satisfy the equation

${\alpha\left\lbrack t_{n} \right\rbrack} = {\ln\left( \frac{{T_{BTMS}\left( t_{n} \right)} - T_{ADJ}}{{T_{BTMS}\left( t_{n - 1} \right)} - T_{ADJ}} \right)}$wherein T_(BTMS)(t_(n)) is the temperature of the brake assembly at timet_(n), T_(BTMS)(t_(n−1)) is the temperature of the brake assembly attime t_(n−1), T_(ADJ) is a tunable parameter. In various embodiments,T_(ADJ) may be a value from 0 to just below the maximum safe brakeassembly temperature (expressed below in various equations as BRAKEHOT).According to various embodiments, by receiving the brake assemblytemperature to determine a peak temperature value, the initial timecondition for estimating the total time to cool a brake assembly may beset to t=0.

Thus, tcool[n] may be found using the below equation:

${t_{Cool}\lbrack n\rbrack} = {{\frac{1}{\alpha\lbrack n\rbrack} \cdot {\ln\left( \frac{{BRAKEHOT} - T_{ADJ}}{{T_{BTMS}\left( t_{n - 1} \right)} - T_{ADJ}} \right)}} - T_{period}}$

In various embodiments, by using the ratio of the temperature of thebrake assembly for two samples taken p number of samples apart, α, maybe determined and satisfy the equation:

${\alpha\left\lbrack t_{n} \right\rbrack} = {\frac{1}{p \cdot T_{period}} \cdot {\ln\left( \frac{{T_{BTMS}\left( t_{n} \right)} - T_{ADJ}}{{T_{BTMS}\left( t_{n - p} \right)} - T_{ADJ}} \right)}}$

Thus, consistent with the above, t_(cool)[n] may be found using thebelow equation:

${t_{Cool}\lbrack n\rbrack} = {{\frac{1}{\alpha\lbrack n\rbrack} \cdot {\ln\left( \frac{{BRAKEHOT} - T_{ADJ}}{{T_{BTMS}\left( t_{n - p} \right)} - T_{ADJ}} \right)}} - {p \cdot T_{period}}}$

In various embodiments, due to various factors (e.g., noise, roundingerrors, etc.), the estimated total time to cool the brake assembly maybe filtered with a low-pass filter to provide a smooth and/or continuousestimation. The particular type of low-pass filter is not particularlylimited and can include any digital filter. For example, variouslow-pass filters can include first order low-pass filters, second orderlow-pass filters, third order low pass filters, etc. Furthermore, thelow-pass filters can include smoothing parameters, such as a tuningparameter.

For example, in various embodiments, the low-pass filter may comprisethe equationt _(Cool) _(_) _(Filt) [i]=t _(Cool) _(_) _(Filt) [i−1]+β·(t _(Cool)[i]−t _(Cool) _(_) _(Filt) [i−1])wherein t_(Cool) _(_) _(Filt)[i] is the filtered estimated total time tocool the brake assembly to a predetermined temperature at time intervali, t_(Cool) _(_) _(Filt)[i−1] is the filtered estimated total time tocool the brake assembly to a predetermined temperature at a timeinterval preceding the time interval i, β is a smoothing constant andt_(Cool)[i] is the unfiltered estimated total time to cool the brakeassembly to a predetermined temperature at time interval i.

As described above, the estimated total time to cool is the period oftime from the present time to the time when the brake assembly reachesthe maximum safe brake assembly temperature (i.e., BRAKEHOT). In variousembodiments, a brake system control unit (“BSCU”) or other processor mayfilter the estimated total time to cool the brake assembly with alow-pass filter for each new period.

In various embodiments after the adjusted estimation is calculated, forexample by a processor (e.g., a processor in a BSCU), various systemsand methods include reporting the adjusted estimation with an outputdevice. According to various embodiments, the output device may be in atleast one of electrical communication and radio frequency (“RF”)communication with the processor, for example, the processor of a BSCU.Without being limited to any theory, it is believed that in variousembodiments, as the estimated temperature converges with the actualtemperature of the brake assembly, the error in estimation is reduced,thus, providing a smoother and a more continuous estimation in outputdevices. Accordingly, because the error in estimation is reduced as theactual temperature approaches the predetermined temperature, minimumcooling time tolerance parameters may be eliminated.

As discussed above, a BSCU or other processor may perform variouscalculations described herein. A BSCU may be in communication with oneor more brake pedals and downstream components that receive commandsfrom the BSCU, either directly or indirectly, to effect and controlbraking. For example, in various embodiments, the BSCU may receive pedalcommands, process the pedal commands, and then command electromechanicalactuator controllers (EMACs) and electromechanical brake actuators(EBAs) or command a shutoff valve (SOV) and/or brake servo valves (BSV)in hydraulic brakes.

Referring to FIG. 1, a system 100 is illustrated according to variousembodiments. System 100 may comprise BSCU 310. BSCU 310 may comprise aprocessor 312, a tangible, non-transitory memory 314, a transceiver 316,and may be communicatively connected to brake temperature monitoringsystem (BTMS) 326, for example through electrical connection 330.Tangible, non-transitory memory 314 may contain logic to allow processor312 to estimate the cooling time of a brake assembly according tovarious embodiments.

In various embodiments, BSCU 310 may evaluate the below equation:

${\alpha\left\lbrack t_{n} \right\rbrack} = {\ln\left( \frac{{T_{BTMS}\left( t_{n} \right)} - T_{ADJ}}{{T_{BTMS}\left( t_{n - 1} \right)} - T_{ADJ}} \right)}$Where T_(ADJ) is a tunable parameter and may take a value from 0 to avalue approaching but less than BRAKEHOT. In various embodiments,T_(ADJ) may be 86 F or 120 F.

According to various embodiments, by BSCU 310 receiving the brakeassembly temperature the time for the brake to cool may then be found byevaluating the equation:

${t_{Cool}\lbrack n\rbrack} = {{\frac{1}{\alpha\lbrack n\rbrack} \cdot {\ln\left( \frac{{BRAKEHOT} - T_{ADJ}}{{T_{BTMS}\left( t_{n - 1} \right)} - T_{ADJ}} \right)}} - T_{period}}$

BSCU 310 may thus receive brake temperature from BTMS 326, for example,continuously or in a random access fashion.

In various embodiments, the estimated time to cool the brake assemblymay be filtered with a low-pass filter that may comprise the equationt _(Cool) _(_) _(Filt) [i]=t _(Cool) _(_) _(Filt) [i−1]+β·(t _(Cool)[i]−t _(Cool) _(_) _(Filt) [i−1])

wherein t_(Cool) _(_) _(Filt)[i] is the filtered estimated total time tocool the brake assembly to a predetermined temperature at time intervali, t_(Cool) _(_) _(Filt)[i−1] is the filtered estimated total time tocool the brake assembly to a predetermined temperature at a timeinterval preceding the time interval i, β is a smoothing constant andt_(Cool)[i] is the unfiltered estimated total time to cool the brakeassembly to a predetermined temperature at time interval i.

Accordingly, in various embodiments, the estimated total time to coolmay be adjusted by the equation using non consecutive temperature valuesp sample apart:

${t_{Cool}\lbrack n\rbrack} = {{\frac{1}{\alpha\lbrack n\rbrack} \cdot {\ln\left( \frac{{BRAKEHOT} - T_{ADJ}}{{T_{BTMS}\left( t_{n - p} \right)} - T_{ADJ}} \right)}} - {p \cdot T_{period}}}$

wherein t_(Cool)[n] is the adjusted estimated time to cool the brakeassembly to a predetermined temperature at time interval n. Exemplarysampling periods according to various embodiments, may include periodsof 5 minutes, 2 minutes, 1 minute, 45 seconds, 30 seconds, and 15seconds.

In various embodiments, the estimated time to cool the brake assemblymay be filtered with a low-pass filter that may comprise the equationt _(Cool) _(_) _(Filt) [i]=t _(Cool) _(_) _(Filt) [i−1]+β·(t _(Cool)[i]−t _(Cool) _(_) _(Filt) [i−1])

wherein t_(Cool) _(_) _(Filt)[i] is the filtered estimated total time tocool the brake assembly to a predetermined temperature at time intervali, t_(Cool) _(_) _(Filt)[i−1] is the filtered estimated total time tocool the brake assembly to a predetermined temperature at a timeinterval preceding the time interval i, β is a smoothing constant andt_(Cool)[i] is the unfiltered estimated total time to cool the brakeassembly to a predetermined temperature at time interval i.

Referring to FIG. 2, a logical flowchart of activation of a system toestimate the time to cool a brake assembly, according to variousembodiments, is illustrated. According to various embodiments,activation method 500 may be used, for example, by a BSCU or otherprocessor to control calculations relevant to the estimation of a timeto cool a brake assembly. According to various embodiments, activationmethod 500 commences at step (step 510). A determination of whether theBTMS temperature reading is valid may be made (step 520). In thatregard, the BTMS temperature reading may be considered valid if the BTMStemperature reading is within a range that is reasonable. If it isdetermined that the BTMS temperature reading is not valid, theestimation of cooling time of the brake assembly is disabled (step 540)and method 500 concludes (step 550). If it is determined that the BTMStemperature reading is valid, then the estimation of cooling time of thebrake assembly is activated (step 530) and then the method may conclude(step 550). In various embodiments, activation method 500 may berepeated continuously. In various embodiments, activation method 500 maybe repeated after a predetermined condition, such as the passing of aperiod of time, when power is supplied to the processor, after a brakingevent, and combinations thereof.

With reference to FIG. 3, a logical flow chart for an output of theestimated time to cool a brake assembly, in accordance with variousembodiments, is illustrated. Method 600 may comprise activating a timeto cool function for a processor such as in a BSCU (step 610). Invarious embodiments, the processor may determine whether the brakeassembly is above a predetermined temperature and not rising (step 620).As used herein, the term “predetermined temperature” may include maximumsafe operating temperatures of braking systems for immediate dispatch,for example, the value BRAKEHOT discussed above. Moreover, the processormay determine if the brake assembly's temperature is rising. If thebrake assembly is not above a predetermined temperature or rising, thenthe output for the time to cool may be set to zero (step 630) and themethod may terminate (step 670). In various embodiments, when the brakeassembly is not above a predetermined temperature, the indication thatthe brakes are cool can be indicated by a variety of methods, such as anvia an indication light, via a display that may show symbols or wordsindicating that the brakes are sufficiently cool, etc.

According to various embodiments, when the brake assembly is above apredetermined temperature and not rising, the processor may compute theestimated time to cool (step 660). In various embodiments, the computingof the estimated time to cool may comprise determining a temperaturedecay coefficient (“α”) of the brake assembly, and calculating anestimated total time to cool the brake assembly to a predeterminedtemperature.

In various embodiments, step 660 may comprise calculating, by theprocessor, an estimated total time to cool the brake assembly to apredetermined temperature based on two consecutive brake assemblytemperature samples. As described above, two consecutive samples may bereferred to a n and n−1 and α may be calculated using the equationdiscussed above:

${\alpha\left\lbrack t_{n} \right\rbrack} = {\ln\left( \frac{{T_{BTMS}\left( t_{n} \right)} - T_{ADJ}}{{T_{BTMS}\left( t_{n - 1} \right)} - T_{ADJ}} \right)}$${t_{Cool}\lbrack n\rbrack} = {{\frac{1}{\alpha\lbrack n\rbrack} \cdot {\ln\left( \frac{{BRAKEHOT} - T_{ADJ}}{{T_{BTMS}\left( t_{n - 1} \right)} - T_{ADJ}} \right)}} - T_{period}}$

wherein T_(BTMS)(t_(n)) is the temperature of the brake assembly at timet_(n), T_(BTMS)(t_(n−1)) is the temperature of the brake assembly attime t_(n−1), T_(ADJ) is a tunable parameter.

In various embodiments, step 660 may comprise calculating, by theprocessor, an estimated total time to cool the brake assembly to apredetermined temperature based on two non-consecutive brake assemblytemperature samples. As described above, two non-consecutive samples maybe referred to as sample n and another sample spaced “p” apart (i.e.,sample n−p) and α may be calculated using the equation discussed above:

${\alpha\left\lbrack t_{n} \right\rbrack} = {\frac{1}{p \cdot T_{period}} \cdot {\ln\left( \frac{{T_{BTMS}\left( t_{n} \right)} - T_{ADJ}}{{T_{BTMS}\left( t_{n - p} \right)} - T_{ADJ}} \right)}}$${t_{Cool}\lbrack n\rbrack} = {{\frac{1}{\alpha\lbrack n\rbrack} \cdot {\ln\left( \frac{{BRAKEHOT} - T_{ADJ}}{{T_{BTMS}\left( t_{n - p} \right)} - T_{ADJ}} \right)}} - {p \cdot T_{period}}}$

wherein T_(BTMS)(t_(n)) is the temperature of the brake assembly at timet_(n), T_(BTMS)(t_(n−p)) is the temperature of the brake assembly attime t_(n−p), T_(ADJ) is a tunable parameter. If the value p is greaterthan 2, for example, the temperatures T_(BTMS)(t_(n)) andT_(BTMS)(t_(n-p)) are non-consecutive

In various embodiments, the estimated time to cool the brake assemblymay be filtered with a low-pass filter that may comprise the equationt _(Cool) _(_) _(Filt) [i]=t _(Cool) _(_) _(Filt) [i−1]+β·(t _(Cool)[i]−t _(Cool) _(_) _(Filt) [i−1])

wherein t_(Cool) _(_) _(Filt)[i] is the filtered estimated total time tocool the brake assembly to a predetermined temperature at time intervali, t_(Cool) _(_) _(Filt)[i−1] is the filtered estimated total time tocool the brake assembly to a predetermined temperature at a timeinterval preceding the time interval i, β is a smoothing constant andt_(Cool)[i] is the unfiltered estimated total time to cool the brakeassembly to a predetermined temperature at time interval i.

With temporary reference to FIGS. 2-3, according to various embodiments,methods 500, 600, and combinations thereof may be repeated to provideupdated information on the estimated time to cool the brake assembly. Invarious embodiments, by repeating various disclosed methods, systems andmethods for determining the cooling time for a brake assembly may adaptcooling profiles based on changing environmental conditions. Forexample, if a pilot takes off with the brakes excessively hot, disclosedsystems and methods may inform the pilot how long he/she must fly withthe gear extended before retraction.

In various embodiments, a hysteresis may be used with BTMS temperaturedata to prevent repeated and constant activation. Accordingly, invarious embodiments, such as those where the cooling time is reported toan output device (e.g., to a control panel in the cockpit), the outputdevice may be prevented from switching on and off repeatedly within aperiod of time.

Various disclosed systems and methods may be independent of whether theBSCU has been turned off after landing. Accordingly, algorithms mayresume once power is restored to disclosed systems allowing forprediction of the time to cool the brake assembly with the new detectedinitial conditions upon re-power up. In various embodiments, this mayallow for more user-friendly systems and methods.

Moreover, disclosed systems and methods according to variousembodiments, may require reduced computation from on-board systems ascompared to conventional methods, therefore making it easier to maintainmemory and other computational equipment. Disclosed methods also reducethe number of tunable parameters when compared to conventional systemsand methods.

As used herein, the meaning of the term “non-transitorycomputer-readable medium” should be construed to exclude only thosetypes of transitory computer-readable media which were found in In reNuijten, 500 F.3d 1346 (Fed. Cir. 2007) to fall outside the scope ofpatentable subject matter under 35 U.S.C. §101, so long as and to theextent In re Nuijten remains binding authority in the U.S. federalcourts and is not overruled by a future case or statute. Stated anotherway, the term “computer-readable medium” should be construed in a mannerthat is as broad as legally permissible.

Benefits, other advantages, and solutions to problems have beendescribed herein with regard to specific embodiments. Furthermore, theconnecting lines shown in the various figures contained herein areintended to represent exemplary functional relationships and/or physicalcouplings between the various elements. It should be noted that manyalternative or additional functional relationships or physicalconnections may be present in a practical system. However, the benefits,advantages, solutions to problems, and any elements that may cause anybenefit, advantage, or solution to occur or become more pronounced arenot to be construed as critical, required, or essential features orelements of the disclosed embodiments. The scope of the claimedembodiments is accordingly to be limited by nothing other than theappended claims, in which reference to an element in the singular is notintended to mean “one and only one” unless explicitly so stated, butrather “one or more.” Moreover, where a phrase similar to “at least oneof A, B, or C” is used in the claims, it is intended that the phrase beinterpreted to mean that A alone may be present in an embodiment, Balone may be present in an embodiment, C alone may be present in anembodiment, or that any combination of the elements A, B and C may bepresent in a single embodiment; for example, A and B, A and C, B and C,or A and B and C.

Systems, methods and apparatus are provided herein. In the detaileddescription herein, references to “one embodiment”, “an embodiment”, “anexample embodiment”, etc., indicate that the embodiment described mayinclude a particular feature, structure, or characteristic, but everyembodiment may not necessarily include the particular feature,structure, or characteristic. Moreover, such phrases are not necessarilyreferring to the same embodiment. Further, when a particular feature,structure, or characteristic is described in connection with anembodiment, it is submitted that it is within the knowledge of oneskilled in the art to affect such feature, structure, or characteristicin connection with other embodiments whether or not explicitlydescribed. After reading the description, it will be apparent to oneskilled in the relevant art(s) how to implement the disclosure inalternative embodiments.

Furthermore, no element, component, or method step in the presentdisclosure is intended to be dedicated to the public regardless ofwhether the element, component, or method step is explicitly recited inthe claims. No claim element herein is to be construed under theprovisions of 35 U.S.C. §112(f), unless the element is expressly recitedusing the phrase “means for.” As used herein, the terms “comprises”,“comprising”, or any other variation thereof, are intended to cover anon-exclusive inclusion, such that a process, method, article, orapparatus that comprises a list of elements does not include only thoseelements but may include other elements not expressly listed or inherentto such process, method, article, or apparatus.

What is claimed is:
 1. A system comprising: a processor, a tangible,non-transitory memory configured to communicate with the processor, thetangible, non-transitory memory having instructions stored thereon that,in response to execution by the processor, cause the processor toperform operations comprising: receiving, by the processor, a firsttemperature of a brake assembly at a first time from a brake temperaturemonitoring system (BTMS); receiving, by the processor, a secondtemperature of the brake assembly at a second time from the BTMS,wherein the second time occurs a fixed period after the first time;determining, by the processor, a temperature decay coefficient (“α”) ofthe brake assembly based on the first temperature and the secondtemperature; and calculating, by the processor, an estimated total timeto cool the brake assembly to a predetermined temperature based on thefirst temperature, the predetermined temperature and α, wherein α isgreater than zero and satisfies an equation${\alpha\left\lbrack t_{n} \right\rbrack} = {\ln\left( \frac{{T_{BTMS}\left( t_{n} \right)} - T_{ADJ}}{{T_{BTMS}\left( t_{n - 1} \right)} - T_{ADJ}} \right)}$wherein T_(BTMS)(t_(n)) is a temperature of the brake assembly at thesecond time (“t_(n)”), T_(BTMS)(t_(n−1)) is a temperature of the brakeassembly at the first time (“t_(n−1)”), and T_(ADJ)is a tuningparameter.
 2. The system according to claim 1, wherein the calculatingthe estimated total time to cool the brake assembly to the predeterminedtemperature comprises an equation${t_{Cool}\lbrack n\rbrack} = {{\frac{1}{\alpha\lbrack n\rbrack} \cdot {\ln\left( \frac{{BRAKEHOT} - T_{ADJ}}{{T_{BTMS}\left( t_{n - 1} \right)} - T_{ADJ}} \right)}} - T_{period}}$wherein t_(Cool)[n] is the estimated total time to cool the brakeassembly to the predetermined temperature (“BRAKEHOT”) at time intervaln, and T_(period) is a length of a sampling period.
 3. The systemaccording to claim 2, further comprising adjusting, by the processor,the estimated total time.
 4. The system according to claim 3, whereinthe adjusting of the estimated total time comprises filtering theestimated total time to cool the brake assembly with a low-pass filter.5. The system according to claim 4, wherein the filtering the estimatedtotal time to cool the brake assembly with the low-pass filter comprisesan equationt _(Cool) _(_) _(Filt) [i]=t _(Cool) _(_) _(Filt) [i−1]+β·(t _(Cool)[i]−t _(Cool) _(_) _(Filt) [i−1]) wherein t_(Cool) _(_) _(Filt)[i] isthe filtered estimated total time to cool the brake assembly to apredetermined temperature at time interval i, t_(Cool) _(_) _(Filt)[i−1]is the filtered estimated total time to cool the brake assembly to apredetermined temperature at a time interval preceding the time intervali, βis a smoothing constant and t_(Cool)[i] is the unfiltered estimatedtotal time to cool the brake assembly to a predetermined temperature attime interval i.
 6. The system according to claim 1, further comprisingan output device in at least one of electrical communication and radiofrequency (“RF”) communication with the processor.